Problem #1

Assume that is the price of a financial contract (on a certain product) and is the total number of contracts outstanding in the market; and is the total amount of Dollars used in buying and selling this product (by all participants in the market). If velocity of money is defined as the number of times it changes hands in buying and selling of a certain contract (or product) then the expression of that velocity of this Dollar amount will be:

a) 
b) 
c) 
d) None of the Above

Problem #2

The value of a quasi-random variable for ten consecutive days is given by:

2.0, 5.0, -1.34, -2.34, 1.85, 0.67, -1.02, 1.25, -0.98, 1.0

Based on the above you make an estimation of the standard deviation of the series. However, from 11 th day onwards and for the next ten days you observe that the value of this variable as:

-0.54, 0.95, 1.20, 1.45, 2.11, 1.0, -2.33, -3.01, 0.20, 1.30

Finally you conclude that the standard deviation of the series:

a) is constant;
b)  varies with time;
c)  oscillates with time;
d) None of the above

Explain your answer.

Problem #3

The current price of a stock is $100. If this stock is assumed to follow a stochastic Weiner process with no drift. The probability that the stock will hit $110 before it hits $75 is approximately:

a)  92%
b)  71%
c)  43%
d) 11%

Problem #4

The probability that it will rain today is 15%. The probability that it will rain tomorrow is 35%. The probability that it will rain today as well as tomorrow is:

(a) 2.63%
(b) 5.25%
(c) 42.85%
(d) None of the above.

Problem #5

A function is completely determined by two parameters, and such that where is the observed values of the function for different sets of values of the parameters and .

However, in a certain system the value of the parameters and are inferred from the observed values of . This is an example of:

(a) forward problem;
(b) inverse problem ;
(c) normal problem;
(d) None of the above;

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